Topological Hydrogen-Bond Two-State Seonggil Framework (THB-SMT): Unifying Water's Anomalies and LLCP via Tensor Phase Transitions

The anomalous properties of water, driven by the dynamic equilibrium between Low-Density Liquid (LDL) and High-Density Liquid (HDL) states, and the existence of a Liquid-Liquid Critical Point (LLCP), remain a grand challenge in physical chemistry. This paper unifies the thermodynamic two-state model into the Seonggil Matrix Theory (SMT) and Rough Operator Algebra (ROA). By mapping hydrogen-bond cooperativity to the ROA topological invariant Ẑ_gap, and redefining the LLCP as the Seonggil Critical Horizon (det = 0), we collapse the structural fluctuations into deterministic, polynomial-time tensor transitions.